Recent years have witnessed a growing body of experimental evidence highlighting the active role of glial cells in modulating neuronal dynamics. Glial cells, including astrocytes and microglia, have been found to influence various aspects of neuronal function, such as regulating neurotransmitter concentrations and ion buffering. Yet, the mechanisms through which glial cells communicate with and affect neighboring neurons remain unclear. In this study, we seek to develop a computational model to explore recent experimental findings which demonstrated that glial cells physically wrap around, or ensheathe, synapses, disrupting the flow of neurotransmitters between pre- and post-synaptic terminals. We start by extending a previous microscale model of the synaptic cleft to explore how different strengths of synaptic ensheathment impact synaptic communication. Our results align with this prior study, showing ensheathment accelerates synaptic transmission while reducing its strength, but we find the previous model underestimates the ability of glial cells to switch off synaptic connections. Building on these findings, we introduce an effective glial cell model that can be integrated into large-scale neuronal networks. We consider a network with highly heterogeneous synaptic parameters, with values determined by the degree of glial proximity. We apply this framework to large networks of exponential integrate-and-fire neurons, extending linear response theory to analyze not only network firing rate distributions but also noise correlations across excitatory neurons. Despite significant heterogeneity in the system, a mean-field approximation accurately captures network statistics. We demonstrate the utility of our model by reproducing experimental findings, showing that increases in glial ensheathment can lead to hyperactivity. Our model also predicts that this ensheathment leads to significant increases in the power spectrum across a range of task-relevant frequencies. Our work supports the idea that synaptic plasticity driven by glial ensheathment is an underappreciated mechanism cortical circuits use to modulate recurrent dynamics.